1. Field of the Invention
The present invention relates generally to a control method of a chemical process such as that used in a chemical reactor. More specifically, the present invention relates to a method for controlling a chemical reactor using a feedforward subroutine for calculating parametric balances responsive to multivariable inputs which takes advantage of system knowledge and a rapid noise filtering subroutine. The present invention is particularly applicable to real time automatic control systems and apparatus and more specifically to a class of controllers utilizing dynamic system prediction techniques employing on-line parametric balances and non-linear modeling. A filter and corresponding filtering method are also disclosed.
2. Brief Discussion of Related Art
In the control art, traditional or classic feedback controllers dominate control practice. Traditional feedback controllers include linear controllers, such as the proportional (P) controller, the proportional-integral (PI) controller, or the proportional-integral-derivative (PID) controller, all of which are discussed below, and non-linear controllers, such as the fuzzy logic (FL) controller. A high level partially block, partially schematic diagram of a hypothetical chemical reactor utilizing P-type feedback control is shown in FIG. 1, which illustrates a process whereby the liquid level in a conical tank 10 is being maintained by controlling the feed rate Vf of the influent liquid. More specifically, a level controller 12 provides signals indicative of the level in tank 10 to a flow controller FC 14, which senses the liquid feed Vf and provides positioning signals to feed control valve 16 to control the liquid feed Vf to the tank 10. It will be noted that, in the system depicted in FIG. 1, the liquid out of the tank is not controlled by the flow controller 14.
It will be appreciated that when the level in the conical tank is above its set-point SP, the controller 14 will reduce the fresh feed to the tank, i.e., decrease Vf, and when it's too low, the controller 14 will increase the flow, i.e., increase Vf. The magnitude of this adjustment is determined by the tuning parameters used, the most important of which is the gain, i.e., the proportional term ("P") in PID. In this case, the gain would be specified is units of (liters/hr)/(% level). By specifying the gain, the operator specifies how much the liquid feed Vf will be adjusted for a change in the percentage (%) deviation of the level in tank 10 from the predetermined set-point SP.
It should also be noted that the other two terms denoted by the term PID are the integral term and the derivative term. The integral term, as its name implies, keeps track of how long the level has been away from the predetermined set-point SP. As the area between the set-point curve and the present valve curve increases, the integral term (I) begins commanding larger changes to the liquid feed Vf. In contrast, the derivative term (D) specifies the adjustment amount for the liquid feed Vf when the level of tank 10 is accelerating or decelerating, e.g., the change in Vf would be a first value when the level of tank 10 is increasing at an increasing rate and a second value different from the first value when the level of tank 10 is increasing at a decreasing rate.
PID is a conventional control strategy that has been around since the 1930's; PID control is still predominant in the chemical manufacturing industry. It will be appreciated that PID control has several advantages, the greatest of which is that it does not require any special knowledge or models of the system; PID control merely requires that the operator have a deft hand at tuning the system. This strength is also its biggest weakness. More specifically, PID control doesn't take advantage of what the operator does know about the system. Thus, for the hypothetical control system illustrated in FIG. 1, the system does not take into account the fact that the tank 10 is conical. As shown in FIG. 1, the conical tank 10 is draining under gravity with the level controller 14 adjusting the flow rate of fresh feed, Vf. Because the tank 10 is conical, the change in the hold-up required to change the level is much greater when the level is high. Intuitively, this presents a problem in that a much larger adjustment to the flow Vf will be required to rectify a level deviation of 1% when the tank 10 is nearly full than when it is nearly empty. For this reason, any single set of tuning parameters for the FC controller 14 will not work for all values of the level set-point SP. Thus, it is generally not be possible to use a single set of tuning parameters for all levels of the tank 10. Therefore, the larger "transitions" from one level to another are principally done manually by the operator since one set of parameters will not work for both the low and high levels of tank 10.
The situation illustrated in FIG. 1 is further complicated if the control system has other control loops operating with respect to the tank 10, i.e., a temperature loop as shown in FIG. 2. In FIG. 2, the temperature 10 is preferably being controlled by adjusting the temperature Tj of the jacket fluid Vj. More specifically, a temperature sensor 18 provides a temperature signal to a temperature controller 20 controlling a heater 22, which heater heats the fluid Vj provided to the jacket 10' of tank 10. To control the tank temperature to 70.degree. C., the temperature controller 20 changes the set-point on the jacket fluid temperature, Tj. It should be noted that controller 14 and 20, although physically isolated from one another, are nonetheless operatively coupled to one another. To help demonstrate the concept of "controller coupling" on this system, assume that the fresh liquid is being fed to tank 10 at 20.degree. C. and assume that the tank fluid density is a function of temperature. Therefore, any change in the feed Vf will affect the temperature of the fluid in tank 10, which will affect the density of the fluid in tank 10, which will subsequently affect the level in tank 10, and so on. As shown in FIGS. 3 and 4, instability can result, as discussed in greater detail below. The relational diagram of FIG. 4 further illustrates controller coupling due to the strong coupling of the level and temperature controllers that occurs through the density of the liquid in the tank 10.
It will be appreciated that the amount of heat transferred to the tank 10 will depend on the temperature difference (T.sub.jacket -T.sub.tank) and the surface area of contact, i.e., the heat exchange surface area. Moreover, the temperature rise in the tank 10 depends on the mass of liquid in the tank and the heat capacity of the liquid. It will be noted that both the surface area for heat exchange and the liquid mass are strong, non-linear functions of tank level; it follows, just by inspection, that any disturbance in or change to the level in tank 10 will upset the temperature of the liquid in tank 10.
Furthermore, assuming that the liquid density is a function of temperature, any change in the temperature of tank 10 will affect the level of liquid in tank 10, which will, in turn, affect the fresh liquid feed Vf, which will further upset the temperature in tank 10. In conventional PID control, this is what is known as controller coupling leading to either sustained oscillations in the system or outright instability of the system. This is shown in FIGS. 3 and 4 for a change of level set-point SP. From these latter Figures, it will be appreciated that while the tuning of controller 14 was acceptable for higher levels of tank 10, the much faster response of the system at lower levels of tank 10 caused severe system instability. The solution to controller coupling for systems with PID control such as illustrated in FIG. 2 is to "detune" one of the controllers 14, 20, i.e., to reduce the ability of controller 20, for example, to control its variable in the interest of keeping the other controllers such as controller 12 from fighting with controller 20. Thus, system stability comes at the price of more drift in addition to a poorer response to a process upset.
FIG. 5 is a generalized schematic diagram of a first gas-phase reactor (GPR) 100 for olefin polymerization products. Polymer is fed to the reactor 100 from the flash drum 110. Gas leaving the top of the reactor 100 is cooled in cooler 114 and recompressed by compressor 140. It will be noted that fresh monomers C2, C3 and hydrogen H2 are then added and the gas is fed back into the GPR 100. Gas also leaves the reactor 100 through the fines cyclone 128 and the polymer discharge valves 130, 132. Gas exiting the discharge valve 130, 132 eventually reaches the ethylene stripper 116, via a teal scrubber 120 and compressor 118, where much of the propylene and propane are removed and returned to the propylene bullet (not shown), while the ethylene and hydrogen H2 are returned to the reactor 100.
FIG. 6 shows the original gas-phase reactor control scheme superimposed on the schematic diagram of FIG. 5. It will be appreciated from inspection of FIG. 6 that the lead control loop uses the calculated value for the homopolymer discharge rate from the flash drum 100 to set the ethylene flow to reactor 100 required to achieve the desired % ethylene in the final product.
In order for the bipolymer produced in GPR 100 to have the right composition of ethylene and propylene, the gas composition must be maintained at the right value. Since the ethylene feed has already been fixed, this is accomplished by adjusting the propylene feed rate according to the reading of the gas controller GC. In particular, hydrogen H2 is controlled to maintain the desired ratio with ethylene. It will be appreciated that the pressure in GPR 100 must be maintained within a prescribed tolerance. Since the ethylene feed is fixed, and since the propylene feed must be adjusted to keep the gas composition on target, the needed control can only be accomplished by adjusting the level of the polymer bed in the reactor 100. It should be noted that the higher the bed level, the more catalyst is provided to the system to react the gas, and vice-versa.
At the bottom of FIG. 6 is a legend listing the measurements taken using system sensors and the variables which are controlled based on these measurements. It will be appreciated that the conventional control scheme, i.e., PID control, produces a basic mismatch in terms of sensing speed and speed of response. It will be noted that the control loop is able to follow changes in the pressure very quickly, yet the pressure is controlled by changing the bed level which changes very slowly. In addition, while the system is able to change the flow rates of the monomers very quickly, the system does not do so because the values for the gas composition change very slowly, and because the homopolymer feed is based on a filtered number.
A block diagram representing the conventional PID control strategy is shown in FIG. 7. As with the conical tank example discussed above, each PID controller in FIG. 7 is self-contained and unable to share information with the others. Another similarity is that these controllers are all "coupled" to the system, as discussed above, which means that they must be tuned to respond slowly to avoid instability. The best example of this is the hydrogen controller 70, which tries to maintain the H2/C2 ratio in the reactor by adjusting the hydrogen feed. However, changes to the C2 feed also affect this ratio. When an upset to either the gas ratio C2/C2+C3)) or the pressure (total gas) occurs, the C2 hold-up will change causing the hydrogen controller 70 to react in an attempt to maintain the ratio H2/C2. However, when the C2 excursion is over, the H2/C2 ratio will be out high on the opposite side, primarily due to the change in the H2 hold-up. It will be appreciated that the hydrogen controller 70, due to the slow tuning required for stability, will require many hours to eliminate the postulated disturbance.
In summary, the conventional control of the gas-phase reactor uses traditional PID controllers with no knowledge of the system controlled or the predictable interactions between the monitored and controlled variables. Because of this, PID control system loops must be tuned to react slowly to thereby minimize the effect of controller coupling. The selection of the ethylene feed as the lead controller, to which changes are allowed only very slowly, is necessary since any disturbance in the ethylene feed will upset all of the other PID controllers regulating the system.
Moreover, traditional feedback controllers do not perform well with processes dominated by dead time and processes having time-variant dynamics. In addition, traditional feedback controllers such as PID controllers do not perform well with multivariable processes, where interactions exist between the process variables. Several predictive control techniques have been developed to address the limitations of traditional feedback controllers, but none of these techniques has displaced the traditional feedback controller from its dominant position in the chemical industry.
It should be noted that the use of linear programming models to implement the control of a process is now conventional. Linear programming models, which mathematically define the relationship between the future changes of controlled variables and current and past changes in manipulated variables, are presently in use to enhance the operation of a process controller. In this context, it should be mentioned that a controlled variable is a process variable that is targeted to be maintained at a desired setpoint whereas a manipulated variable is a variable which is adjusted to drive the controlled variable to the target value. In any commercial process disturbances will occur external to the process which may cause instability, decrease efficiency and change product quality unless the process is controlled to respond in real time to the unmeasured disturbances. An unmeasured disturbance to the process may arise e.g., from an ambient temperature change, from a change in product formulation, or from an unexpected change in demand for products. In addition, such a process has system constraints such as temperature, pressure and flow rate which place limits on the process variables and must also be accounted for during control of the process.
Existing adaptive control methods such as employed in the adaptive Pole Placement controller and the Minimum Variance controller are promising approaches to accomplish needed control tasks. However, they suffer from two potentially crippling limitations: (1) computational complexity, which limits their feasibility in multivariable applications; and (2) sensitivity to the choice of the input-output delays and model order selection. There has been considerable research recently in the development of adaptive controllers that attempt to overcome these limitations. A major focus has been the development of extended horizon predictive control methods. U.S. Pat. Nos. 5,301,101, 5,329,443, 5,424,942 and 5,568,378, which patents are incorporated herein by reference for all purposes, disclose various forms of horizon controllers and corresponding methods. The summary presented below summarizes the material from the background sections of several of the above captioned patents.
Dynamic matrix control (DMC) is a process control methodology using process models to compute adjustments in manipulated variables based on a prediction of future changes in controlled variables. The basic concept of dynamic matrix control is to use known time domain step response process models to determine changes in manipulated variables which minimize or maximize a performance index over a specified time horizon. A time sequence of manipulated variable changes for each manipulated variable is computed based on the response of the process predicted by the time domain step response models such that the performance index is optimized. It will be appreciated that the DMC controller by Cutler and Ramaker is based on an approximated step response model. Therefore, the DMC controller can be only applied to open loop stable systems.
High performance, computationally efficient real-time dynamic controller software and hardware are required for use in complex multi-input, multi-output, nonlinear, time-varying systems that are operating in challenging environments. In particular, there is a need for efficient control methods for dynamic systems having large numbers of system inputs and outputs, which overcome modeling uncertainties and unmeasurable external perturbations to the controlled systems.
The simplest predictive control methods, such as the Minimum Variance and the Generalized Minimum Variance methods, take into account the fact that the dynamic system has an input-output delay D. Control inputs are chosen to make the system match some desired trajectory in D steps ahead. Recently, predictive controllers that consider time horizons beyond the system input-output delay (extended horizon predictive controllers) have been used in many engineering applications. The motivation for doing this is two-fold. First, the input-output delays of a dynamic system are usually not known in advance, and if the time delays are incorrectly estimated, or the delays are time varying as system operation progresses, then the system input-output stability can suffer. Second, for high performance controller designs with fast sampling, the resulting sampled dynamic system often has nonminimum phase zeros (having zeros outside the unit circle). In this case, when the choice of control is only based on the beginning of the system step response, the controller often does not perform well.
Inside all extended horizon predictive and adaptive predictive controllers is a "predictor" that estimates future values of certain quantities related to the system outputs, based on current and past values of inputs and outputs. If the prediction horizon k extends beyond the system delay, D, then the set of (k-D) future inputs (u(t),u(t+1), . . . , u(t+k-D)) must be assumed. Different predictive and adaptive predictive controllers make different assumptions (or place different constraints) on these `extra` inputs. The predicted system outputs are then used to compute the control inputs, based upon some criterion. Several extended horizon predictive controllers have been developed previously. They differ in how the set of future controls is chosen. These controllers include: the Extended Horizon Adaptive Control (EHC), the Receding Horizon Adaptive Control (RHC), the Control Advance Moving Average Controller (CAMAC), the Extended Prediction Self-Adaptive Control (EPSAC), the Generalized Predictive Controller (GPC), the Model Predictive Heuristic Control (MPHC), and the Dynamic Matrix Control (DMC).
The EHC predictive controller developed by Ydstie is based on an Auto-Regressive Moving-Average with auxiliary input (ARMAX) model description of the dynamic system, as described in Goodwin and Sin. The set of k future controls is chosen by minimization of the control effort, subject to the constraint that the k-step ahead predicted output is equal to some desired value. In the EHC, two implementation approaches have been used: extended horizon and receding horizon implementations. In the extended horizon implementation, the set of k future controls is implemented sequentially and updated every k samples. In the receding horizon implementation of the EHC (i.e., the RHC), only the first control in the set is applied to the system. At the next sampling instant, the whole set of k future controls is computed and again only the first one is used. In the extended horizon implementation, the EHC can stabilize both open loop unstable and nonminimum phase systems. The RHC, however, cannot stabilize an open loop unstable system in general.
The CAMAC controller developed by Voss et al, differs from the EHC controller in the selection of the set of future controls. In the CAMAC controller, all k future controls are assumed to be constant. This choice assures offset-free tracking performance in steady state, even without an integral action. The CAMAC controller can also be used for both receding horizon and extended horizon implementations. Again, the CAMAC controller can fail if the open loop system is unstable. Both the EHC and the CAMAC controllers have considered the output at only one future point in time.
The GPC controller developed by Clarke et al extends this idea by allowing the incorporation of multi-slep output predictions. The set of k future controls in the GPC is determined by the minimization of a quadratic cost function of predicted output tracking errors and controls, up to a horizon value into the future. The GPC is implemented in a receding horizon manner, as in the RHC controller. The GPC controller is effective for both open loop unstable and nonminimum phase systems. Because a Controlled Auto-Regressive Integrated Moving-Average (CARIMA) model is used to model the dynamic systems and to predict the output, the GPC controller always contains an integrator. The GPC controller includes the EPSAC controller as a special case.
The MPHC controller by Richalet et. al. makes output predictions, based on an approximated impulse response model. On the other hand, the DMC controller by Cutler and Ramaker are based on an approximated step response model. Therefore, both MPHC and DMC controllers can be only applied to open loop stable systems. However, it should be mentioned that the DMC controller can stabilize a nonminimum phase system.
In short, the model-based "horizon" controllers now being introduced to control chemical reactors such as gas-phase reactors promise greatly improved control both at steady-state and during transitions. The horizon controllers and corresponding method accomplish this partly through the use of feed-forward calculations to determine what the eventual steady-state value of the manipulated variable will be and referencing all "overshoot" and "undershoot" moves relative to this predicted value. It will be appreciated that this feature makes horizon controllers very fast in responding to an upset; however, these model-based horizon controllers are not optimized for dealing with both steady state and transient modes of operation. It will also be appreciated that this feature makes horizon controllers very fast in responding to an upset, but at the cost of making these controllers very susceptible to noise in the signals that are used for making the feed-forward calculation(s). With respect to the latter, these signals need to be smooth to avoid excessive swinging of the manipulated variable, which can be destabilizing to the rest of the plant. Preferably, generation of these "smooth" signals must be accomplished as rapidly as possible.
One of the simplest signal filters available is the low-pass filter having the form: EQU Xf(t)=Xf(t-1)+FIL*[X(t)-Xf(t-1)] (1)
It involves taking the difference between the current measurement, X(t), and the last value of the filtered signal, Xf(t-1), and only moving the filtered signal some fraction of this distance, determined by the value of FIL. Note that for FIL=1, no smoothing is done, while for FIL=0, the raw signal is ignored entirely. For values less than 1, the smaller the value, the greater the smoothing, but the longer the delay in response to a true change in the underlying signal. Note also that the low-pass filter always changes the value of Xf(t) relative to Xf(t-1) except when X(t) happens to exactly equal Xf(t-1). This means that it transmits all the noise, although with a reduced magnitude. Therefore, the only way to get a very smooth filtered signal from a noisy source is to have a small value of FIL and to put up with a slow response.
What is needed is a method for controlling a chemical reactor, e.g., a gas-phase reactor, which employs on-line parametric balances, e.g., pressure and/or density balances, and non-linear modeling to simultaneously control the gas composition, pressure, and chemical content in the final product. What is also needed is a method for rapidly filtering noise from raw data produced by system sensors to minimize the number of unneeded control operations initiated by the control method.